I was a bit sloppy in two blocks near the ends of
Wholeness Charts 2-2 and 2-5. See corrections at Changes
to Charts 2-2 and 2-5. As I noted in the text, it may be best not to get
too deeply into Chart 2-2, as it is primarily a summary of classical
variational mechanics, and the changes made here relate to subtle aspects of
that theory, which are not so relevant for QFT.

Allan Tameshtit

23

2

Aug 6, 2015

Box
2-2. My purpose in this box was to give a derivation of (B2-2.3) that was
much simpler than that in other books. There are some subtleties involved,
but it is best not to worry about them until after you have mastered QFT. If
at that time, you feel up to it, check out Box2_2_comments

27

2

Apr 6, 2016

Eq
(2-37). Some further explanation plus some changes related to (2-37) are in
order. See Comments on
(2-37).

Tom Bartholet

30

2

Aug 6, 2015

For
versions prior to July 2015, this was OK. For the July 2015 version,
equations (2-42) and (2-43). The “i” subscript on delta would be better as a
superscript. Ultimately, it doesn’t really matter, but it helps the parallel
with (2-44) if “i” is superscripted.

54

3

Aug 17, 2015

The
k’s in the numerators (two places) in the second line of (3-52) should have superscripts,
not subscripts. (3-52) as written, strictly speaking, is still correct, as
there are two k's with subscript i multiplied, which equal two k's with
superscript i multiplied. But this correction should eliminate confusion.

Steffen Leger

61

3

May 8, 2017

Mid
page, after 2nd paragraph after “Caveat”.

If
normal ordering were only used in QFT to get a Delta E energy level (as that
is all that is relevant in classical theory) one might concede some
justification for it. However, as one will see in Chap 4 (pg. 112 after “End
of Derivation”), it is also commonly invoked to get the correct charge
operator for spin 1/2 fields. Otherwise, the vacuum would have an infinite
charge. Since we have no theories where that can simply be subtracted, it is
hard to justify use of normal ordering for charge derivation, and one’s confidence
in it is further eroded.

Note
that on pg. 112, I present an alternative derivation to the charge operator
that does not depend on normal ordering.

73

3

June 16, 2016

1st
line after (3-122). The first “factor” in (3-122) is GF of (3-120). The
second “factor” in (3-122) is HF of (3-120). In teaching a QFT course, I was
asked by a student “where did the GF and HF of (3-120) go?”

Lou Biegeleisen

74

3

Mar 2, 2016

Last
line on page: After the comma, insert we have the Cauchy integral formula -

Tom Bartholet

76

3

Sept 29, 2016

The
line after (3-140). It is correct as is, but maybe easier to understand if we
change “the route” to which route (loop) -

79

3

Apr 1, 2016

In
(3-150), change partial time derivative to total derivative. In next line,
after “field,” insert with the aid of Box 2.1, pg. 22,

2nd
paragraph of Conclusion #1: Insert at
beginning of paragraph: For Fig. 4-5(b), .
After “Changing v”, insert (without aligning it with S) After “Therefore,”, insert in Fig. 4-5(b) -

Tom Bartholet

142

5

June 16, 2016

(5-35)
top row. This is correct as it is, since dummy indices can be used
interchangeably. However, it can be easier to understand if the mu and nu
superscripts on the epsilons on the RHS of each equal signed are switched.

Tom Bartholet

142

5

June 16, 2016

(5-36).
The r’s after the second equal sign should be underlined, as there is no sum.

Tom Bartholet

147

5

June 16, 2016

(5-50).
The summations should only be over r, not k. The integral is over the range of k.

Tom Bartholet

158

5

May 16, 2016

Wholeness
Chart 5-4, 4th row, 2nd column on page. Put a bar over
rho. Two places. (rho is an expectation value not an operator here.)

Eq.
(6-14). The arguments for the vector and tensor on the RHS of their
respective equal signs should not have a Lambda^alpha_beta before the x^beta. Two places. (And it might look
neater to change the beta on the x
to an alpha, but not essential.)

Tom Bartholet

176

6

Aug 22, 2016

Eq
(6-41). The first minus sign (before N_b) should be a plus sign.

Tom Bartholet

184

7

June 22, 2016

Eq.
(7-8). The minus sign in front of “e” should be a plus.

186

7

Oct 27, 2016

(7-19):
Comparing with (7-16), one might wonder about the change in order of the QFT
field operators (photon and fermion) after the equal sign. The order here is
not important, as fields associated with different types of particles
commute. Amu commutes
with psi here.

Tom Bartholet

198

7

Sept 22, 2016

Sentence
just above Sect 7.5.2, change “(7-62)” to - (7-63) -.

Tom Bartholet

205

7

May 9, 2017

First
paragraph following (7-82), “C3D4= - D3C4”
should be “C3D4= - D4C3”

Tom Bartholet

211

7

Nov 11, 2016

(7-109):
The first three terms on the second line should have the Nc
operator in front of them.

(7-110).
The last term in the top row should have the Nc
operator in front.

Tom Bartholet

217

8

May 9, 2017

(8-9),
after 2nd equal sign: The Sfi should be inside the Sigma and
all f except that in the bra should
be primed.

Tom Bartholet

231

8

May 9, 2017

(8-74) and (8-75) both need to insert “i” in front of the expression for SF

Tom Bartholet

231

8

Jan 16, 2017

3rd
line after (8-79): Change “denotes antiparticles.” to is sometimes used in Feynman diagrams for
virtual antiparticles. It is just a symbol. The overbar here is not related
to adjoint fields.

Vasudev Godbole

235

8

May 9, 2017

(8-89): Insert a delta function with argument zero on
the RHS outside the integral.

Tom Bartholet

239

8

May 12, 2017

First line: insert “e” after equal sign.

Tom Bartholet

247

8

June 16, 2016

2nd
paragraph up from bottom of page. At end of sentence, add or to interactions that can be renormalized
away (not treated in this text).

271

10

May 8, 2017

Sect.
10.2.4. Actually, the Fulling-Davies-Unruh effect is not related to the 1/2
quanta, the higher order corrections, nor the 3 virtual particle bubbles, but
to a more advanced concept in QFT related to time dependent Hamiltonians.
Finding it in an experiment would not really be a proof of zero point energy
in the usual 1/2 quanta sense.

274

10

June 16, 2016

(10-8),
top row. Don’t hold up your study of QFT by spending much time on this fairly
advanced material. Someday I may re-write this section with these changes.
Each 1/2, should be multiplied by a delta(0), i.e., a Dirac delta function
with argument zero. This also applies to every relation on the next 2-3 pages
with a 1/2 term. See links on book website for Continuous Solutions for
reasons why. From that one could also see why comments in this part of the
text for single 1/2 quanta particle wave packet in “all space” should refer
to “unit volume”.

281-283

10

June 16, 2016

WhCh
10-2. Wherever there is a continuous solutions form with 1/2 inside the
integral, it should be a multiplied by a factor delta(0), i.e., a Dirac delta
function with argument zero. See links on book website for Continuous
Solutions for reasons why.

Comment (not correction) on (12-17) RHS: The
superscript (2) might be confusing. Here the notation, along with the
subscripts, means we take the 2nd order in e form of the
amplitudes but use the modified versions for e, photon propagator, and vertex
gamma matrix (as described in under bracket note).

Tom Bartholet

323

13

Oct 13, 2017

Fig. 13-1: Under the first diagram, insert ieo2 before Pi.
Under the 2nd diagram, insert ieo2
before Sigma. In the 3rd diagram, insert ieo3 before Lambda.

Add to text above the figure: Applying Feynman’s rules
in Fig. 13-1, excluding the incoming and outgoing particles, yields the
amplitudes under each diagram, where the symbols are defined in (13-1) to
(13-3).

Tom Bartholet

328

13

Oct 13, 2017

7th line down on page: Change “each of
these terms must equal zero” to - these terms must sum to zero -

Tom Bartholet

337a

13

Oct 13, 2017

(13-83): both lines need a summation over r symbol
inserted

(13-84): needs same summation over r inserted

Tom Bartholet

337a

13

Oct 13, 2017

Paragraph after (13-84): the operator atilde_r(k) should have a summation over r
symbol in front of it. Same for adagger-tilde_r(k).

2nd paragraph on pg beginning with
“Moreover..”: Move this entire sentence down below eq (14-86) and just above
the paragraph beginning “Bottom line”. Also, at the end of the sentence, add in light of (14-86). -

We will
retain only retain the leading log terms (see Sect. 15.1.15, pg. 378), with Λ2 >> k2. As shown in
the appendix (see Chap
15 addition to appendix), the first two terms in the integral of (15-44)
and the two directly below them are of order 1, so relative to Λ2 (and k2, since we are assuming k2 >> m2
where m2>>1), they
can be ignored. Doing this, we get (15-45).

Tom Bartholet

384

15

May 8, 2017

I
have recently realized that cut-off regularization has a more obvious reason
for why it doesn’t work. It is not Lorentz invariant, as the upper limit on
our integral (max energy) is not Lorentz invariant (energy for the same
object changes as seen in different frames). The other three regularization
methods discussed are all Lorentz invariant, and they all produce the correct
result.

-In order for this to work, we have to change the
propagator of the so-called heavy particle a bit. We give it a negative sign
and keep the “m” in the numerator
without changing it to “Λ”, like we do in the denominator. This
makes the whole procedure work mathematically (which is our goal), even
though it tarnishes the analogy to a heavy particle propagator a bit. -

(7-110),
2nd line: Boxes with 8, 9, and 10 in them should be above the
terms, rather than below them.

221

8

May 9, 2017

(8-24): “Bhabba” should be “Bhabha”

Tom Bartholet

224

8

May 9, 2017

(8-42), “r” subscript of “ν” should be primed

Tom Bartholet

225

8

May 9, 2017

Fig. 8-3 would probably be better with the first
vertex on each side labeled x2
and the second x1, as it
would track the text better. But it is common to not write in the coordinate
labels at each vertex in Feynman diagrams, so the reader needs to get
accustomed to the practice.

Box 8-1. At the end of the box, add “Do Prob. 18 for
more insight on this.” Then, add, at the end of the chapter.

Prob. 18. Draw the mass shell for a photon. Suppress
the k2 and k3 dimensions, to make it
easier. That is, plot E vs k1. Does it touch the
origin? Are the sides of the shell, for a photon, straight lines? Does the
mass shell for a massive particle like that shown in Box 8-1 approach that of
a photon asymptotically for very high E
(speed approaching c)?

Tom Bartholet

256

9

May 12, 2017

Fig. 9-1, RHS: Reverse the arrow on the lower line to
make it a positron.

(9-7): It may be easier to follow if the SF(p) gamma^mu were moved to after the gamma^nu. Given that these
factors are inside the trace, it doesn’t really matter, but the whole thing
tracks Fig. 9-5 better if it is done this way.

Tom Bartholet

261

9

May 12, 2017

(9-13): Put a factor of 1/(2 pi)2 after the
equal sign.

Tom Bartholet

262

9

May 12, 2017

Line above (9-16): After “natural” insert - and
Heaviside-Lorentz -

Tom Bartholet

264

9

Sept 30, 2016

Next
to last bullet near bottom of page: delete space after “Compton”

285b

10

May 24, 2017

Prob. 1, 2nd line: The quantity inside the
bra should not be the complex conjugate of the quantity inside the ket, but
the same thing. The bra notation implies the quantity shown inside, when
expressed mathematically, has the complex conjugate taken.

Tom Bartholet

282

10

May 24, 2017

Last row, 2nd column: The quantity inside
the bra should not be the complex conjugate of the quantity inside the ket,
but the same thing. The bra notation implies the quantity shown inside, when
expressed mathematically, has the complex conjugate taken.

Tom Bartholet

285

10

May 24, 2017

Section 10.12, Appendix E: It is clearer if whenever
the term “delta function“ is used, it is replaced with “Dirac delta function”
(so as not to confuse with the Kronecker delta).

Paragraph after (13-40): After “typically)”,
insert - , in the sense that it gives
rise to a corresponding vertex in a Feynman diagram -

Tom Bartholet

331

13

Oct 13, 2017

2nd line after (13-42): before “photon”
insert external -

Tom Bartholet

332

13

Oct 13, 2017

(13-49): Right near end of equation, for Sigma_c, the p argument should have a slash through
it.

Tom Bartholet

334

13

Oct 13, 2017

1st line after (13-56) In the expression
right after “Also,”, delete the - i
-.

Tom Bartholet

337

13

Oct 13, 2017

(13-78), 4th line down: operator adagger_r”
needs an argument (k”).

Tom Bartholet

340

14

Dec 7, 2017

4th line down below Fig 14-1 title: change
“second” to - third row -

Tom Bartholet

340

14

Dec 7, 2017

Eq (14-1): The factor in front of the integral needs
to be divided by (2pi)4.

Tom Bartholet

343

14

Dec 7, 2017

Sect. 14.2.1, Step VI), first line: Delete “the Taylor
expansion of the”. This is not wrong, but one reader thought it confusing.

Tom Bartholet

369

14

Dec 7, 2017

Wholeness Chart 14-5, column (IV), 2nd row:
change comma to non-subscript so it can be seen.

Tom Bartholet

371

14

Aug 6, 2015

Page
heading should be “Section 14.9 Chapter Summary”. Heading as shown should
have “mu” instead of a box (2 places). Computer glitch in 2nd ed.
Not in 1st.

373

14

Dec 7, 2017

Probs. 3 and 4: In “e0 ”, the superscript zero should be a subscript.

Tom Bartholet

379

15

Jan 15, 2018

(15-29): The derivatives in the top row should be
enclosed in parentheses, so the epsilon = 0 does not apply to the factors of
epsilon and epsilon square.

Tom Bartholet

382

15

Jan 15, 2018

(15-48) to (15-49): We considered the first two terms
in the second line of (15-48) negligible. In the newly added (not in text,
online) appendix used to go from (15-44) to (15-45), we showed these terms
equal i pi/6 5/18.

Tom Bartholet

385

15

Jan 15, 2018

2nd line below (15-57): put a minus sign in
front of Lambda squared.

Tom Bartholet

394

15

Jan 15, 2018

2nd line below (15-111): Change “electrons”
to fermions -. (For time upward, Fig. 15-2
would show an electron and a positron.) Also change “are” to approach and equal signs to approximately equal
signs.

Tom Bartholet

399

15

Jan 15, 2018

2nd line after (15-133): after “each”,
insert integral -.

Tom Bartholet

403

16

Oct 25, 2017

5th line up from bottom: Change “.)” to - ). -

John Davidson

414

16

Oct 25, 2017

2nd line above (16-48): underlining on mu
mu subscripts should be raised.